It is possible to “delete” find my from your iPhone. Technically it isn’t deleted but a 15yr old isn’t going to know this bit of esoteric info. You remove it like you would any other App so it seems deleted.
If you got an iPhone with say only 64GB storage, she could have a point about lack of storage and/or lack of data allowances as find my uses data when out and not at home using WiFi.
You might want to consider an iCloud+ subscription to add more storage and then activate family sharing so she can access the iCloud+ storage and you can track and see how much is being used.
You also might want to consider upgrading her data allowance on her cell phone package if you want her to have find my active everytime she is out of the house.
Finally, if the objection based on logistics is masking an objection based on privacy, you may have to compromise with her on how to reassure you she is ok without her feeling constantly watched, monitored and tracked. My teens refused find my and with a teen you know they will turn it on as you stand over them and then as soon as they are 5mins away will turn it off. This will then cause battles of will, grounding, defiance, worse behaviour etc.
I instead said how about you send me texts saying you have arrived at friends house, or to gym, or at bus stop with ETA…and told them if after dark and walking to call & we can chat while they walk home.